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# Pythagoras for dummies. A quick and easy guide to work out an unknown side using Pythagoras.

## Pythagoras Fast Method Video

What is Pythagoras used for?

Pythagoras (or Pythagoras Theorem) is used to calculate an unknown side length of a right angled triangle.

What information do you need to know to carry out Pythagoras?

You will need to know the lengths of 2 other sides. If you are given a side and an angle then the question is likely to be a trigonometry question.

Is Pythagoras complicated?

No, it can be done in 3 simple steps without using any algebra:

**1) First square the two side lengths that are given in the question.**

**2) Either:**

**Add squares together if you are finding the longest side (aka the hypotenuse)**

**Or find the difference if you are not working out the longest side.**

**3) Square root the answer from step 2. You will probably have to use your calculator to do this.**

What is the formula for Pythagoras?

a² + b² = c². Where a, b and c are the 3 sides with c being the longest side. If you are in a high math group then you should really use this formula. However, in this hub we will use the 3 steps above.

**Example 1**

Work out the length of the missing side in this right angled triangle (x).

1) First square the two side lengths that are given in the question.

6² = 36

12² = 144

2) Either:

Add squares together if you are finding the longest side (aka the hypotenuse)

Or find the difference if you are not working out the longest side.

36 + 144 = 180 (Add them as x is the longest side)

3) Square root the answer from step 2. You will probably have to use your calculator to do this.

√180 = 13.4 cm to 1 decimal place.

**Example 2**

Calculate the length of the missing side in this right angled triangle (x).

1) First square the two side lengths that are given in the question.

8² = 64

7² = 49

2) Either:

Add squares together if you are finding the longest side (aka the hypotenuse)

Or find the difference if you are not working out the longest side.

64 - 49 = 15 (Take them as y is not the longest side).

3) Square root the answer from step 2. You will probably have to use your calculator to do this.

√15 = 3.9 cm to 1 decimal place.